Jesse asked in Science & MathematicsChemistry · 9 months ago

Describe how Charles’ Law, Boyle’s Law, and Gay-Lussac’s Law work together to make the combined gas law.

Using the ideal gas law, PV = nRT, in which R is always 8.31 , what pressure is required to hold 4.10 moles of nitrogen gas in a 3.2 L container at a temperature of 37 degrees Celsius? Show your work.

A tank holding 7.80 L of gas is at a pressure of 9.80 atm. If the temperature and number of gas particles do not change, what is the new pressure at a volume of 5.3 L?

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• 9 months ago

Combined gas law .....

You can get the combined gas law with just Boyle's law and Charles's law.

P1V1 = P2V2 and V1/T1 = V2/T2

Which is convenient because there is no such thing as "Gay-Lussac's law." There is Gay-Lussac's law of combining volumes, but that's something else entirely. The notion that P1/T1 = P2/T2 is somehow attributed to Gay-Lussac is a mistake, one that has be propagated for years. Gay-Lussac followed up on the work of Jacques Charles. Charles never published his work, but Gay-Lussac did, attributing it to Charles. This is why in France and much of Europe it is called the "Law of Charles and Gay-Lussac." If you want to ascribe someone's name to the relationship between pressure and temperature at constant volume, then it should be Amontons's Law.

The ideal gas equation (PV=nRT) came about through the work of Claperyon (1834) and tied together Boyle's law, Charles's law and Avogadro's law.

If you are going to mention the gas constant, then you must include the units and maybe another significant digit. The gas constant, R, can be expressed in a number of pressure units.

Your choice of R will determine the units of P

R = 0.08206 Latm/molK ........ atm

R = 8.314 LkPa/molK ............ kPa .........R = 8.314 J/molK

R = 0.08314 Lbar/molK ......... bar

R = 62.36 Ltorr/molK ............. torr (aka mm Hg)

Also keep in mind that pressure is always a dependent variable. It depends on the volume of the gas, the number of moles of particles, and the absolute temperature.

P = nRT / V

P = 4.10 mol x 8.314 LkPa/molK x 310. K / 3.2L

P = 3300 kPa .................. rounded to two significant digits

P1V1 / T1 = P2V2 / T2 .......... combined gas law

P1V1 = P2V2 ......................... constant T .... Boyle's law

P2 = P1V1 / V2 ...................... solve for P2

P2 = 9.80 atm x 7.80L / 5.3L

P2 = 14 atm ........................... the answer is limited to two significant digits